We have obtained Fourier-resolved spectra of the black-hole binary 4U 1543-47 in the canonical states (high/soft, very high, intermediate and low/hard) observed in this source during the decay of an outburst that took place in 2002. Our objective is to investigate the variability of the spectral components generally used to describe the energy spectra of black-hole systems, namely a disk component, a power-law component attributed to Comptonization by a hot corona and the contribution of the iron line due to reprocessing of the high energy (E greater than or approx, equal to 7 keV) radiation. We find that i) the disk component is not variable on time scales shorter than approx. 100 seconds, ii) the reprocessing emission as manifest by the variability of the Fe K(alpha) line responds to the primary radiation variations down to time scales of approx. 70 ms in the high and very-high states, but longer than 2 s in the low state, iii) the low-frequency QPOs are associated with variations of the X-ray power law spectral component and not to the disk component and iv) the spectra corresponding to the highest Fourier frequency are the hardest (show the flatter spectra) at a given spectral state. These results questions the models that explain the observed power spectra as due to modulations of the accretion rate only.